Question

what is the measure of angle tas?

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, \(10x + 9=8x + 9\).

Step2: Solve for \(x\)

Subtract \(8x\) from both sides: \(10x-8x + 9=8x-8x + 9\), which simplifies to \(2x+9 = 9\). Then subtract 9 from both sides: \(2x+9 - 9=9 - 9\), getting \(2x=0\), so \(x = 0\).

Step3: Find the measure of \(\angle TAS\)

Substitute \(x = 0\) into the expression for \(\angle TAS\) (either \(10x + 9\) or \(8x + 9\)). Using \(10x+9\), when \(x = 0\), we have \(10\times0+9=9\).

Answer:

\(9^{\circ}\)